The break-in was reported shortly after 6 a.m., according to the Los Angeles Police Department. Officers responded to a local hospital, where they spoke with a patient who had suffered a gunshot wound.
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Police then went to the home in the 15300 block of Valley Vista Boulevard, where two men armed with handguns had entered through the rear of the residence and demanded money, wallets and purses.
Several shots were fired at one point, but it was unclear if the residents also fired weapons, investigators said. The intruders fled with the victims' unspecified property in a black Ford Expedition and a black BMW.
The man who was shot in the arm transported himself to the hospital, the LAPD said. A second victim, who sustained a graze wound, was treated at the scene.
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A description of the suspects was not available.
Nearby residents said the home is owned by a Lancaster doctor who rents it out on a short-term basis, adding that parties attended by 300-400 young people are often held there.
A section of Sherman Oaks Avenue remained closed Wednesday afternoon as the investigation continued at the scene.